Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
A New Method for Developing Signature Algorithms on Finite Non-commutative Algebras
Authors: Moldovyan A. A., Moldovyan D.N.
Keywords: Finite associative algebras, non-commutative algebras, discrete logarithm problem, hidden logarithm problem, multivariate cryptography, public-key cryptoscheme, digital signature, post-quantum signature algorithm
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Keywords: Finite associative algebras, non-commutative algebras, discrete logarithm problem, hidden logarithm problem, multivariate cryptography, public-key cryptoscheme, digital signature, post-quantum signature algorithm
Abstract
A new method for developing signature schemes on finite non-commutative associative algebras is introduced. A signature algorithm is developed on a 4-dimensional algebra defined over the ground field $GF(p)$. The public key element and one of the signature elements represent vectors calculated using exponentiation operations in a hidden commutative group. Decomposition of the algebra into commutative subalgebras is taken into account while designing the algorithm. The method extends the class of algebraic digital signature schemes and opens up the possibility of developing a number of practical post-quantum digital signature algorithms, the main merit of which is comparatively small size of the public key, secret key, and signature.St. Petersburg Federal Research Center of the Russian
Academy of Sciences (SPC RAS),14 Liniya V.O., 39,
St.Petersburg, 199178, Russia
E-mail: ,
Academy of Sciences (SPC RAS),14 Liniya V.O., 39,
St.Petersburg, 199178, Russia
E-mail: ,
DOI
https://doi.org/10.56415/basm.y2022.i1.p56Fulltext
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Contents
- Continuous Extensions On Euclidean Combinatorial Configurations
- Subordination and superordination for certain analytic functions associated with Ruscheweyh derivative and a new generalised multiplier transformation
- Different Types of Compact Global Attractors for Cocycles with a Noncompact Phase Space of Driving System and the Relationship Between Them
- A New Method for Developing Signature Algorithms on Finite Non-commutative Algebras
- Properties of coverings in lattices of ring topologies
- Equilibria in Pure Strategies for a Two-Player Zero-Sum Average Stochastic Positional Game
- Morita Contexts, Preradicals and Closure Operators in Modules
- A self--similar solution and the tanh--function method for the kinetic Carleman system
